9. Ja. Let F be a field. Prove that ... + a,r"|a, E Fand a, + a,+ + a, = 0). Ix] = {a, + a,x + the set of all polynomials in F(x] such that the sum of the coefficients is zero, is an ideal of F[x]. b. Prove or disprove that /[x] is a principal ideal. %3D
9. Ja. Let F be a field. Prove that ... + a,r"|a, E Fand a, + a,+ + a, = 0). Ix] = {a, + a,x + the set of all polynomials in F(x] such that the sum of the coefficients is zero, is an ideal of F[x]. b. Prove or disprove that /[x] is a principal ideal. %3D
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 32E
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